Question

How do you express \[y=\dfrac{2}{3}x-2\] in standard form?

Answer 1

Hint: The standard form of a function is the form that has all the variable terms and constant terms. To express the given equation in its standard form, we need to shift all the variable and constant terms to one side of the equation leaving only zero to the other side.

Complete step-by-step answer:
We are asked to express the equation \[y=\dfrac{2}{3}x-2\] in its standard form. We know that the standard form of a function is the form that has all the variable terms and constant terms. To do this, we need to take all the terms to one side of the equation.
Adding 2 to both sides of the given equation, we get
\[\Rightarrow y+2=\dfrac{2}{3}x-2+2\]
Simplifying the equation, we get
\[\Rightarrow y+2=\dfrac{2}{3}x\]
Subtracting \[\dfrac{2}{3}x\] from both sides of the above equation, we get
 \[\Rightarrow y+2-\dfrac{2}{3}x=\dfrac{2}{3}x-\dfrac{2}{3}x\]
Simplifying the equation, we get
\[\Rightarrow -\dfrac{2}{3}x+y+2=0\]
The above equation has all its terms in its left hand side and the right side of the equation has only zero. Thus it is the standard form of the given equation.
The standard form of the given equation is \[-\dfrac{2}{3}x+y+2=0\]. As we can see that the degree of the equation is one, it is a linear equation.

Note: Expressing in standard forms also includes simplifying the expression. Standard forms of equations are very useful while solving some questions. For example, in coordinate geometry, while solving questions of conics. we need to express the equation in its standard form, and check whether it satisfies conditions for a particular conic or not.